Our efforts here are the simplest extension of WZDR. One could consider multi-component dark matter where only a portion couples to the dark sector, but with enhanced interaction [1]}, [2]}. In such a “fractional WZDR+” setup, one would expect that a similar phenomenology to the above would be found, but constraining a product of interaction strength and interacting dark matter fraction, leaving a large degeneracy. In the tightly coupled limit, the interacting dark matter fraction would acoustically oscillate, rather than feel a slight friction during infall. In this limit, one would similarly expect a good fit, but trading a precise value of \(\Gamma _0\)  for a precise value of the interacting fraction \(f_\chi \)  to fit the value of \(S_8\) . We leave the details to future work.
